Quite often, actually. This is why we pad our estimates.
It's inescapable, in that providing a description of the problem that is precise enough to generate a perfectly accurate estimate is very close to actually just being the solution. As you do the work, the estimated time to do the work approaches the time already spent doing it.
But a lot of customers want essentially the same thing--probably a glorified CRUD app with pretty management dashboards, and a workflow that exactly parallels the all-paper workflow first designed in 1965. If you do that sort of thing often enough, eventually you get a feel for how much it costs, even with the variation across customers.
Medicine has a great advantage over software in that decades of hyper-detailed hospital billing--set up in an effort to maximize the yield of patient cash-ectomies in the face of insurer pushback--can now be subjected to statistical analysis. All those diagnosis and billing codes can be plugged back in to the billing databases to discover the median cost for the care to treat a particular ailment. It isn't so hard to then say that I am willing to pay the median actual cost, plus an X% margin for the hospital, even if the actual cost is less, provided that the hospital also eats the difference if the cost is actually more. On average, if everyone did this, the hospital still makes enough money to stay in business.
Some diagnoses in particular, such as the one every woman on the planet is likely to get an average of 2 times during her lifetime, probably while between the ages of 16 and 50, are particularly amenable to cost averaging. If you can't quote the cost of a hospital childbirth to a patient with months of lead time, including the possibility of emergency surgery, you deserve what happens to you when every actuary can crank out an answer using a pocket calculator within 15 minutes of being asked to do so. You know how much it costs. You just don't want to say, because that takes away your leverage to charge more.
But ethically, the care provider should probably not have that leverage, because if they haggle, people can die. If you cure a disease that affects 3 people in 100000, we can talk about the size of your bonus. But if you (the hospital) are on your 3rd laparoscopic gallbladder removal in the same week, and still don't know how much it costs, I want the power to set the price taken away from you.